An integer ambiguity candidate solution determination method

Abstract

The application provides a method for determining integer ambiguity candidate solutions, comprising the following steps: determining integer ambiguities that meet a predetermined condition in an ambiguity search space; calculating a weight corresponding to each integer ambiguity; and determining a weight proportion function value corresponding to each integer ambiguity according to the weight, and screening out a predetermined number of integer ambiguities that meet the condition as ambiguity candidate solutions.

Description

[0001] The original basis for this divisional application is patent application No. 2025114819261, filed on October 16, 2025, entitled "A method for resolving ambiguity in RTK and INS combined positioning". Technical Field

[0002] This invention relates to the field of combined RTK (Real-Time Kinematic) and INS (Inertial Navigation System) positioning technology, and particularly to ambiguity resolution for combined RTK and INS positioning. Background Technology

[0003] In RTK or RTK-integrated navigation and positioning systems, as well as PPP-AR and PPP-AR-integrated navigation and positioning systems, regardless of the solution strategy or process, it is unavoidable to fix the ambiguity. The premise of correctly fixing the ambiguity is to obtain a set of candidate solutions (integer ambiguity candidate solutions) containing the correct solution based on a series of accuracy indicators. Only by applying different search strategies on this basis can the correct or relatively correct ambiguity fixing value be obtained.

[0004] Traditional methods fix the ambiguity to an integer value. While this aligns with the theoretical characteristics of the parameter (due to the periodicity of satellite carrier signals), in interference-prone environments (significant multipath effects or the use of low-cost equipment), it easily fixes the ambiguity to other integers near the true value. This causes the observed carrier phase to jump by cycles, resulting in meter-level deviations in the positioning results—unacceptable for a precise positioning system. Therefore, a method for determining integer ambiguity candidate solutions is needed to select appropriate candidate solutions from the pool of ambiguity candidates affected by environmental factors in reality.

[0005] Furthermore, on the one hand, there are differences in understanding among those skilled in the art; on the other hand, the applicant studied a large number of documents and patents when making this invention, but due to space limitations, not all details and contents were listed in detail. However, this does not mean that the present invention does not possess the features of these prior art. On the contrary, the present invention already possesses all the features of the prior art, and the applicant reserves the right to add relevant prior art to the background art. Summary of the Invention

[0006] The present invention is made in view of the above-mentioned problems, in order to solve one or more defects existing in the prior art, and at least provide an advantageous alternative.

[0007] According to one aspect of the present invention, a method for determining candidate solutions for integer ambiguity is provided, characterized by comprising the following steps: determining integer ambiguities that meet predetermined conditions for screening in an ambiguity search space; calculating the weight corresponding to each integer ambiguity; and determining the weight ratio function value corresponding to each integer ambiguity based on the weight, and screening out a predetermined number of integer ambiguities that meet the conditions as candidate solutions for ambiguity.

[0008] According to some embodiments of the present invention, by weighting the members of the ambiguity candidate solutions that are affected by the environment, the errors that originally exist in the system can be absorbed, the influence of non-Gaussian noise that cannot be solved by the traditional algorithm (ILS) can be suppressed, and the serious deviation in positioning caused by the traditional method fixing the ambiguity to an erroneous integer value that deviates greatly from the true value due to environmental interference can be prevented or mitigated.

[0009] The embodiments of the present invention are applicable to complex observation environments such as urban canyons, and can meet the requirements for high-precision and high-reliability navigation and positioning in such environments. They can be applied to high-precision navigation and positioning scenarios such as surveying and mapping engineering, aerospace, and intelligent driving.

[0010] The description of the above advantages in this invention does not imply that the technical solution of the independent claim must simultaneously possess all of the above advantages. Attached Figure Description

[0011] Figure 1 This is a schematic flowchart of an ambiguity resolution method for RTK and INS combined positioning according to one embodiment of the present invention.

[0012] Figure 2 This illustrates one embodiment of the invention for obtaining a baseline vector floating-point solution. ) and its variance-covariance matrix ( ), floating-point ambiguity ( ) and its variance-covariance matrix ( ), and the cross-covariance matrix between floating-point ambiguity and the floating-point solution of the baseline vector ( and A schematic diagram of ( ).

[0013] Figure 3 This is a schematic diagram illustrating a method for obtaining ambiguity candidate solutions according to one embodiment of the present invention. Detailed Implementation

[0014] Specific embodiments of the present invention will now be described with reference to the accompanying drawings. These descriptions are exemplary and intended to enable those skilled in the art to implement the embodiments of the present invention, and are not intended to limit the scope of protection of the present invention. No content essential for actual implementation but irrelevant to understanding the present invention is described in the description.

[0015] The specific embodiments of the present invention will be further described in detail below with reference to the accompanying drawings, but this does not constitute any limitation on the present invention. Components that, although related to the specific implementation of the embodiments of the present invention, are irrelevant to understanding the present invention are not shown in the drawings, and these components are not described in the specification. These components can be made using various techniques now known or to be known in the future, all of which are within the scope of protection of the present invention. The specific embodiments of the present invention are not a limitation on the claims; the scope of the patent is defined by the claims. The features in the embodiments of the specification cannot be used to limit the scope of the claims.

[0016] Figure 1 This is a schematic flowchart of an ambiguity resolution method for RTK and INS combined positioning according to one embodiment of the present invention.

[0017] like Figure 1 As shown, firstly in step S101, the baseline vector floating-point solution of the RTK and INS combined positioning system is obtained ( ) and its variance-covariance matrix ( ), floating-point ambiguity ( ) and its variance-covariance matrix ( ), and the cross-covariance matrix between floating-point ambiguity and the floating-point solution of the baseline vector ( and ).

[0018] Various methods existing in the technology can be used to obtain the baseline vector floating-point solution, floating-point ambiguity, and its variance-covariance matrix and cross-covariance matrix of the RTK and INS combined positioning system, which will not be elaborated here.

[0019] Figure 2 An embodiment according to the present invention is shown, in which the baseline vector floating-point solution is obtained in step S101 ( ) and its variance-covariance matrix ( ), floating-point ambiguity ( ) and its variance-covariance matrix ( ), and the cross-covariance matrix between floating-point ambiguity and the floating-point solution of the baseline vector ( and A schematic diagram of ( ).

[0020] like Figure 2 As shown, in step S201, observations from the RTK and INS combined positioning system are acquired. For example, in an urban canyon environment, the receiver first acquires the observations from the RTK and INS combined positioning system. According to one embodiment, the observations include GNSS pseudorange observations, carrier phase observations, ephemeris files, and INS state measurements.

[0021] Then, in step S202, the measurement innovation value at the current time (set as time k) is calculated based on the obtained GNSS pseudorange observations and INS state measurements. At the same time, the predicted state value at the current moment is calculated.

[0022] According to one implementation, the current state vector is defined as follows: (1) in: This refers to the INS error state, including attitude error. Speed ​​error Position error accelerometer zero bias gyroscope zero bias , where n represents the value in the n-frame (i.e., the navigation coordinate system) and b represents the value in the b-frame (i.e., the vehicle coordinate system).

[0023] It is a single-difference ambiguity vector. Indicates from the base station To mobile station superscript The satellite system is represented by G: GPS, R: GLONASS, E: GALILEO, C: BDS, J: QZSS, I: IRNSS. Indicate frequency (e.g., GPS: L1, L2, L5, GLONASS: L1, L2, GALILEO: E1, E5a, E5b, E6, BDS: B1, B2, B3, QZSS: L1, L2, L5, IRNSS: L5, S).

[0024] According to one implementation, this measurement innovation value Calculate as follows: (2) in: This represents the double difference operator; They represent the first satellite and the first One satellite; It is a dual differential carrier phase; It is a double-difference pseudorange; It is the two-difference geometric distance predicted by INS; and They represent the first satellite and the first Single-difference ambiguity of a satellite.

[0025] According to one implementation, the current state prediction value is determined as follows: (3) in: Here is the state transition matrix. For process noise, It is the state estimate of the previous time step (i.e., time step k-1).

[0026] Those skilled in the art will readily understand that when k=1, it is necessary to set an initial prior estimate. To obtain the state estimate at the first time step. The state estimate at the first time step can be obtained using Kalman filtering. As the filtering process iterates, the state estimates at times 2, 3, 4, ..., k-2, k-1 are obtained sequentially. This is the state estimate at time k-1, and it is used in the calculation of the state estimate at time k.

[0027] Next, in step S203, the prior covariance is calculated. According to one implementation, the prior covariance is calculated as follows. : (4) in: It is the posterior covariance estimate of the previous time step, i.e., time step k-1. for The transpose of a matrix. For process noise The variance matrix; Similar to the state estimate, it is calculated through Kalman filtering iterations from the previous time step (time step k-2) and participates in the posterior covariance matrix of the next time step (time step k). The calculation.

[0028] Next, in step S204, the measurement prediction value is obtained based on the state prediction value. According to one embodiment, this can be performed as follows: (5) in: For the observation matrix, To observe noise.

[0029] Then, calculate the Kalman gain. : (6) in: To measure noise The variance matrix.

[0030] Then, in step S205, based on the residual between the measured predicted value and the measured innovative value (i.e. ), to obtain state estimates And based on the prior covariance at the current moment Calculate the posterior covariance at the current time. .

[0031] According to one implementation, the following is based on the Kalman gain. The residual of the measured innovation value is used to calculate the state estimate at the current time. : (7) According to one implementation, it can be based on the prior covariance at the current moment as follows: Calculate the posterior covariance at the current time. : (8) pass The statistical correlation and error propagation characteristics between the current state estimates can be obtained, which can then be used as the variance-covariance matrix for the subsequent calculation of the floating-point solution of the current baseline vector. Variance-covariance matrix of floating-point ambiguity and their mutual covariance matrices and The foundation.

[0032] Finally, in step S206, the state estimate at the current time is used. The corresponding variance-covariance matrix is ​​then corrected on the baseline vector predicted by INS to obtain the floating-point solution of the baseline vector at the current time and its variance-covariance matrix. Floating-point fuzziness and its variance-covariance matrix The cross-covariance matrix between floating-point ambiguity and the floating-point solution of the baseline vector and (These are collectively referred to as required parameters).

[0033] This step can be performed in various ways known to those skilled in the art.

[0034] This method directly estimates INS-related and GNSS-related errors, and can model state variables as random walk models, thus reducing the computational difficulty of state prediction values.

[0035] Back Figure 1In step S102, the floating-point ambiguity and its variance-covariance matrix are subjected to ambiguity decorrelation processing to obtain a set of decorrelated floating-point ambiguities.

[0036] According to one implementation, the LAMBDA algorithm can be used to perform an integer Gaussian transform (also known as a Z-transform) on the ambiguity parameters and their variance-covariance matrix. This transform is achieved through an integer transform matrix Z, aiming to reduce the correlation between ambiguity parameters. After the transform, the variance-covariance matrix ( The absolute values ​​of the off-diagonal elements in the matrix are significantly reduced, meaning the correlation between ambiguities is significantly decreased, thus making the matrix closer to diagonalization. This decorrelation process yields a set of mapped floating-point ambiguities with lower correlation. This improves the efficiency of fuzzy search.

[0037] By using the LAMBDA algorithm for ambiguity decorrelation and candidate solution search, the search space is effectively reduced, the computational complexity is decreased, and the algorithm's running efficiency is improved, making it more suitable for navigation application scenarios with high real-time requirements.

[0038] Then, in step S103, a predetermined number (t in this paper) of ambiguity candidate solutions are obtained by using the decorrelated floating-point ambiguity set and the variance-covariance matrix.

[0039] Figure 3 A schematic diagram of a method for obtaining ambiguity candidate solutions according to one embodiment of the present invention is shown.

[0040] According to one implementation, the fuzzy search space after decorrelation processing is first obtained in step S301.

[0041] According to one implementation, firstly, the floating-point ambiguity vector after decorrelation processing is used... and the corresponding variance-covariance matrix The true solution is defined by the chi-square distribution, which includes the integer fuzziness vector after downcorrelation processing. (area) , where a is the preset confidence level (e.g., 99.7%) and n is the dimension of ambiguity.

[0042] Then, the true solution of the integer fuzziness vector after correlation reduction is determined according to the one-dimensional variance. Integer range of each component: ,in k The coefficient corresponding to the confidence level (e.g., 3 corresponds to 99.7%). and The numbers are rounded down and rounded up, respectively, to obtain the fuzzy search space after the correlation reduction process.

[0043] It should be noted that obtaining the fuzzy search space after downcorrelation processing is optional, not mandatory, but obtaining the fuzzy search space after downcorrelation processing can improve the efficiency of the search.

[0044] Then, in step S302, integer ambiguities that meet predetermined conditions are determined in the ambiguity search space. According to one embodiment, integer values ​​in the ambiguity search space after decorrelation processing are obtained sequentially through a sequential conditional least squares search, and the inequality satisfying the above (i.e., ...) is calculated. The set of integer ambiguity vectors after decorrelation processing. Through inverse transformation... For each integer ambiguity vector obtained after downcorrelation processing ( The transformation is performed to obtain the integer fuzzyness vector that participates in the screening. ).

[0045] Then in step S303, according to the quadratic residual form of each integer ambiguity vector and the floating-point ambiguity vector ( This means that the weighted distance between the integer ambiguity vector and the floating-point ambiguity vector is used to arrange each integer ambiguity vector from smallest to largest.

[0046] Then, in step S304, the weights of each integer ambiguity vector participating in OIA screening are calculated sequentially using the weight calculation function.

[0047] The weight calculation function is: (9) in: For the first The weights corresponding to the integer ambiguity vectors; Let be the i-th integer ambiguity vector in the original solution space; is the Laplace distribution scaling factor.

[0048] It is a weighted norm. It is the quadratic residual of the floating-point ambiguity and the i-th integer ambiguity vector.

[0049] Finally, in step S305, a predetermined number of integer ambiguities that meet the conditions are selected as ambiguity candidate solutions based on the weights.

[0050] According to one implementation, based on the weights, the weight percentage function value corresponding to each integer ambiguity is determined until the weight percentage function value of the (t+1)th integer ambiguity vector is found to be less than a threshold. Then, the first t integer ambiguity vectors that meet the requirements are retained to form a candidate ambiguity solution. Here, t is a positive integer.

[0051] The weighting percentage function value is: (10) The screening stop condition is: (11) in: This is the weighted cumulative threshold for the OIA test.

[0052] When the weight ratio of the latest candidate solution Stop when the time is right, and obtain the first t candidate solutions.

[0053] According to the embodiments of the present invention, the OIA test and reasonable candidate solution screening strategy can effectively eliminate erroneous ambiguity candidate solutions, thereby controlling the accuracy of ambiguity candidate values ​​participating in the solution process, and providing effective protection for improving positioning accuracy and enhancing the robustness of the solution.

[0054] Next, in step S104, the receiver position coordinates are calculated using the ambiguity candidate solution, and the residual between these receiver position coordinates and the receiver position coordinates predicted by INS is calculated. Utilizing this residual To update the weights of integer ambiguity candidate solutions in S103.

[0055] According to one implementation method, the residual is calculated as follows: : (12) in: Substitute the fixed solution of the receiver coordinates calculated in the constructed double-difference observation equation into the i-th candidate combination; The receiver position coordinates predicted by INS; According to one implementation, the weights of the ambiguity candidate solutions are updated as follows: First, based on the residuals Obtain the INS impact factor The value of INS impact factor. The value is used to update the weights of the ambiguity candidate values.

[0056] (13) (14) in, These parameters are selected empirically and are used to adjust the range of influence of the INS pre-integration results on the updated weights. According to one implementation, they can be obtained by fitting historical data. According to another implementation, they can be simply set to a predetermined number, which can be a number between 0.95 and 1.05. It is a weighted norm. It is the quadratic residual of the floating-point ambiguity and the i-th integer ambiguity vector.

[0057] According to an embodiment of the present invention, by adding the INS influence factor to the weight factor calculation formula based on the Laplace distribution and re-deriving its partial derivative with respect to the floating-point solution of ambiguity, it is possible to better handle noisy data with heavy-tailed characteristics, reduce the influence of outliers on ambiguity estimation, thereby significantly improving the accuracy of ambiguity estimation and thus enhancing the positioning accuracy of the integrated navigation system.

[0058] Then, in step S105, the first t integer candidate solutions are weighted and fused using the updated weights of the integer ambiguity candidate solutions to obtain the ambiguity estimate. ) and baseline vector estimates ( ).

[0059] According to one implementation, weighted fusion is performed as follows to obtain the ambiguity estimate ( ) and baseline vector estimates ( ): (1) Ambiguity estimate (15) (2) Baseline vector estimate (16) Finally, in step S106, the final solution is determined based on the ambiguity estimate and the baseline vector estimate.

[0060] According to one implementation, the trace of the variance-covariance matrix of the ambiguity estimate and the baseline vector estimate is used... ) and the trace of the variance-covariance matrix of the baseline vector floating-point solution ( Compare them, in Greater than When, the baseline vector estimate ( ) is taken as the final solution, otherwise the baseline vector floating-point solution ( () as the final solution.

[0061] According to one implementation, the variance-covariance matrix of the baseline vector estimate is first calculated. According to one implementation, the variance-covariance matrix of the baseline vector estimate is determined as follows: (17) in: (18) in, A unit diagonal matrix; (19) It is a weighted norm.

[0062] Then, the variance-covariance matrix of the baseline vector estimates ( ) and the variance-covariance matrix of the floating-point solution of the baseline vector ( Compare the traces of ) Output baseline vector estimate when Output the baseline vector floating-point solution.

[0063] By utilizing the embodiments of the present invention, the partial derivatives of the floating-point solutions of ambiguity are cleverly employed, which can better handle noisy data with heavy-tailed characteristics, reduce the impact of outliers on ambiguity estimation, thereby significantly improving the accuracy of ambiguity estimation and thus enhancing the positioning accuracy of the integrated navigation system.

[0064] The method of this invention can be applied to the BeiDou satellite navigation system.

[0065] The method of this invention improves the accuracy and reliability of ambiguity estimation in integrated navigation systems by optimizing the ambiguity decorrelation, candidate solution screening and fusion process. It can be applied to high-precision navigation and positioning scenarios, such as surveying and mapping engineering, aerospace, and intelligent driving.

[0066] The numbering of the method steps in this invention is for ease of description only and is not a specification or explanation of their execution order. Those skilled in the art should understand that the order of these steps can be adjusted or some steps can be executed in parallel according to the actual situation.

[0067] It should be noted that the specific embodiments described above are exemplary. Those skilled in the art can devise various solutions inspired by the disclosure of this invention, and these solutions all fall within the scope of this invention and its protection. Those skilled in the art should understand that this specification and its accompanying drawings are illustrative and not intended to limit the scope of the claims. The scope of protection of this invention is defined by the claims and their equivalents. This specification contains multiple inventive concepts; terms such as "preferredly," "according to a preferred embodiment," or "optionally" indicate that the corresponding paragraph discloses an independent concept. The applicant reserves the right to file divisional applications based on each inventive concept.

Claims

1. A method for determining candidate solutions with integer ambiguity, characterized in that, Includes the following steps: In the fuzzy search space, determine the integer fuzzinesses that meet the predetermined conditions for selection; Calculate the weight corresponding to each integer ambiguity; as well as Based on the weights, determine the weight percentage function value corresponding to each integer ambiguity, and select a predetermined number of integer ambiguities that meet the conditions as candidate ambiguity solutions.

2. The method according to claim 1, characterized in that, The weights are determined as follows: （9） in: For the first The weights corresponding to the integer ambiguity vectors; For floating-point ambiguity; Let be the i-th integer ambiguity vector in the original solution space; The Laplace distribution scaling factor; It is a set of n-dimensional integer ambiguity vectors; Denotes the weighted norm. It is the quadratic residual form of the floating-point ambiguity and the i-th integer ambiguity vector. This represents the quadratic residual form between the floating-point ambiguity and the z-th integer ambiguity vector.

3. The method according to claim 2, characterized in that, Based on the aforementioned weights, a predetermined number of integer ambiguities that meet the conditions are selected as candidate ambiguity solutions as follows: Sort the integer fuzziness levels participating in the filtering from smallest to largest; Based on the weights, determine the weight percentage function value corresponding to each integer fuzziness participating in the screening; The search continues until the weight ratio function value of the (t+1)th integer ambiguity vector is less than the threshold. The first t integer ambiguity vectors are then used to form a ambiguity candidate solution, where t is a positive integer.

4. The method according to claim 3, characterized in that, The weighting function value is determined as follows: （10） Where j is used to identify the j-th integer ambiguity vector. The weight corresponding to the j-th integer ambiguity vector; i is the index variable in the summation operation, used to traverse the integer fuzzyness vectors from 1 to j to calculate the sum of the weights corresponding to these vectors.

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